How do you solve the following linear system: $y = 3 x - 2, 14 x - 3 y = 0$ $y = 3x - 2 , 14x - 3y = 0$ ?

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How do you solve the following linear system: $y = 3 x - 2, 14 x - 3 y = 0$ $y = 3x - 2 , 14x - 3y = 0$ ?

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Answer 1 · 2018-05-08T03:00:32

The solution is $(- \frac{6}{5}, - \frac{28}{5})$ $(-6/5,-28/5)$ or $(- 1.2, - 5.6)$ $(-1.2,-5.6)$ .

Explanation:

Solve the linear system:

$Equation 1 :$ $"Equation 1":$ $y = 3 x - 2$ $y=3x-2$

$Equation 2 :$ $"Equation 2":$ $14 x - 3 y = 0$ $14x-3y=0$

The solution is the point $(x, y)$ $(x,y)$ that the two lines have in common, which is the point of intersection. I'm going to use substitution to solve the system.

Equation 1 is already solved for $y$ $y$ . Substitute $3 x - 2$ $3x-2$ for $y$ $y$ in Equation 2 and solve for $x$ $x$ .

$14 x - 3 (3 x - 2) = 0$ $14x-3(3x-2)=0$

Expand.

$14 x - 9 x + 6 = 0$ $14x-9x+6=0$

Simplify.

$5 x + 6 = 0$ $5x+6=0$

Subtract $6$ $6$ from both sides.

$5 x = - 6$ $5x=-6$

Divide both sides by $5$ $5$ .

$x = - \frac{6}{5}$ $x=-6/5$ or $- 1.2$ $-1.2$

Substitute $- \frac{6}{5}$ $-6/5$ for $x$ $x$ in Equation 1. Solve for $y$ $y$ .

$y = 3 (- \frac{6}{5}) - 2$ $y=3(-6/5)-2$

Expand.

$y = - \frac{18}{5} - 2$ $y=-18/5-2$

Multiply $2$ $2$ by $\frac{5}{5}$ $5/5$ to get an equivalent fraction with $5$ $5$ as the denominator.

$y = - \frac{18}{5} - 2 \times \frac{5}{5}$ $y=-18/5-2xx5/5$

$y = - \frac{18}{5} - \frac{10}{5}$ $y=-18/5-10/5$

Simplify.

$y = - \frac{28}{5}$ $y=-28/5$ or $- 5.6$ $-5.6$

The solution is $(- \frac{6}{5}, - \frac{28}{5})$ $(-6/5,-28/5)$ or $(- 1.2, - 5.6)$ $(-1.2,-5.6)$ .

graph{(y-3x+2)(14x-3y+0)=0 [-6.366, 4.73, -8.243, -2.696]}

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How do you solve the following linear system: $y = 3 x - 2, 14 x - 3 y = 0$ $y = 3x - 2 , 14x - 3y = 0$ ?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you solve the following linear system: y=3x−2,14x−3y=0y = 3x - 2 , 14x - 3y = 0?

1 Answer

Explanation:

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Impact of this question

How do you solve the following linear system: $y = 3 x - 2, 14 x - 3 y = 0$ $y = 3x - 2 , 14x - 3y = 0$ ?